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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue (10): 9-    DOI: 10.1631/jzus.2005.A1055
    
Hollow dimension of modules
ORHAN Nil, KESKİN TÜTÜNCÜ Derya
Department of Mathematics, University of Hacettepe, Beytepe 06532, Ankara, Turkey
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Abstract  In this paper, we are interested in the following general question: Given a module M which has finite hollow dimension and which has a finite collection of submodules Ki (1≤i≤n) such that M=K1+...+Kn, can we find an expression for the hollow dimension of M in terms of hollow dimensions of modules built up in some way from K1,...,Kn? We prove the following theorem: Let M be an amply supplemented module having finite hollow dimension and let Ki (1≤i≤n) be a finite collection of submodules of M such that M=K1+...+Kn. Then the hollow dimension h(M) of M is the sum of the hollow dimensions of Ki (1≤i≤n) if and only if Ki is a supplement of K1+...+Ki−1+Ki+1+...+Kn in M for each 1≤i≤n.

Key words： Hollow dimension      Supplement submodule     
Received: 16 January 2005     
CLC:  O177  
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ORHAN Nil
KESKİN TÜTÜNCÜ Derya
Cite this article:

ORHAN Nil, KESKİN TÜTÜNCÜ Derya. Hollow dimension of modules. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(10): 9-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A1055     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I10/9

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